{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:43:07Z","timestamp":1740156187750,"version":"3.37.3"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,5,27]],"date-time":"2024-05-27T00:00:00Z","timestamp":1716768000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004686","name":"Deanship of scientific research, King Faisal University","doi-asserted-by":"publisher","award":["A081"],"id":[{"id":"10.13039\/501100004686","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric functions and generalized Bessel functions of the first kind. Specific constraints are imposed on the parameters to ensure the inclusion of the confluent hypergeometric function within the analytic function class. The coefficient bound of the class is used to determine the inclusion properties of integral operators involving generalized Bessel functions of the first kind. Different results are observed for these operators, depending on the specific values of the parameters. The results presented here include some previously published findings as special cases.<\/jats:p>","DOI":"10.3390\/sym16060662","type":"journal-article","created":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T07:48:49Z","timestamp":1716882529000},"page":"662","source":"Crossref","is-referenced-by-count":1,"title":["Sufficient Conditions for Linear Operators Related to Confluent Hypergeometric Function and Generalized Bessel Function of the First Kind to Belong to a Certain Class of Analytic Functions"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4540-1601","authenticated-orcid":false,"given":"Saiful R.","family":"Mondal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4500-6655","authenticated-orcid":false,"given":"Manas Kumar","family":"Giri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore, Vellore 632014, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9582-6662","authenticated-orcid":false,"given":"Raghavendar","family":"Kondooru","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Vellore, Vellore 632014, India"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,27]]},"reference":[{"key":"ref_1","unstructured":"Rainville, E. (1960). Special Functions, The Macmillan Co., Ltd."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1296","DOI":"10.1016\/j.camwa.2011.12.077","article-title":"Integral transforms of functions to be in certain class defined by the combination of starlike and convex functions","volume":"63","author":"Raghavendar","year":"2012","journal-title":"Comput. Math. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"211","DOI":"10.24193\/subbmath.2020.2.04","article-title":"Inclusion properties of hypergeometric type functions and related integral transforms","volume":"65","author":"Wani","year":"2020","journal-title":"Stud. Univ. Babes-Bolyai Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1738","DOI":"10.37256\/cm.5220244039","article-title":"Inclusion results on hypergeometric functions in a class of analytic functions associated with linear operators","volume":"5","author":"Giri","year":"2024","journal-title":"Contemp. Math."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"227","DOI":"10.36045\/bbms\/1432840860","article-title":"On the Janowski convexity and starlikeness of the confluent hypergeometric function","volume":"22","author":"Ali","year":"2015","journal-title":"Bull. Belg. Math. Soc. Simon Stevin"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/s10476-017-0203-8","article-title":"On confluent hypergeometric functions and generalized Bessel functions","volume":"43","author":"Bohra","year":"2017","journal-title":"Anal. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1090\/S0002-9939-1990-1017006-8","article-title":"Univalence of Gaussian and confluent hypergeometric functions","volume":"110","author":"Miller","year":"1990","journal-title":"Proc. Am. Math. Soc."},{"key":"ref_8","first-page":"73","article-title":"Univalence and convexity properties for confluent hypergeometric functions","volume":"36","author":"Ponnusamy","year":"1998","journal-title":"Complex Var. Theory Appl."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Baricz, \u00c1. (2010). Generalized Bessel Functions of the First Kind, Springer. Lecture Notes in Mathematics Vol. 1994.","DOI":"10.1007\/978-3-642-12230-9"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1080\/10652460903516736","article-title":"Starlikeness and convexity of generalized Bessel functions","volume":"21","author":"Baricz","year":"2010","journal-title":"Integral Transform. Spec. Funct."},{"key":"ref_11","first-page":"165","article-title":"Relations between the generalized Bessel functions and the Janowski class","volume":"21","author":"Kanas","year":"2018","journal-title":"Math. Inequal. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1016\/j.aml.2011.06.014","article-title":"Certain geometric properties of normalized Bessel functions","volume":"24","author":"Prajapat","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s11139-015-9724-6","article-title":"Geometric properties of some Lommel and Struve functions","volume":"42","author":"Baricz","year":"2017","journal-title":"Ramanujan J."},{"key":"ref_14","first-page":"3987231","article-title":"Univalent and starlike properties for generalized Struve function","volume":"20","author":"Farzana","year":"2016","journal-title":"Int. J. Math. Math. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s13370-018-0625-x","article-title":"On the Janowski class of generalized Struve functions","volume":"30","author":"Noreen","year":"2019","journal-title":"Afr. Mat."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Sim, Y., Kwon, O., and Cho, N.E. (2018). Geometric properties of Lommel functions of the first kind. Symmetry, 10.","DOI":"10.3390\/sym10100455"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.4134\/BKMS.2015.52.3.1035","article-title":"Hardy space of Lommel functions","volume":"52","author":"Yagmur","year":"2015","journal-title":"Bull. Korean Math. Soc."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Din, M.U., Raza, M., Xin, Q., Yal\u00e7in, S., and Malik, S.N. (2022). Close-to-Convexity of q-Bessel\u2013Wright Functions. Mathematics, 10.","DOI":"10.3390\/math10183322"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.4153\/CJM-1987-054-3","article-title":"Univalent and starlike generalized hypergeometric functions","volume":"39","author":"Owa","year":"1987","journal-title":"Can. J. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0022-247X(86)90329-X","article-title":"On the order of starlikeness of hypergeometric functions","volume":"113","author":"Ruscheweyh","year":"1986","journal-title":"J. Math. Anal. Appl."},{"key":"ref_21","unstructured":"Duren, P.L. (1983). Univalent Functions, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1090\/S0002-9939-1957-0086879-9","article-title":"Univalent functions and nonanalytic curves","volume":"8","author":"Goodman","year":"1957","journal-title":"Proc. Amer. Math. Soc."},{"key":"ref_23","first-page":"141","article-title":"Starlike properties for convolutions involving hypergeometric series","volume":"52","author":"Ponnusamy","year":"1998","journal-title":"Ann. Univ. Mariae Curie-Sklodowska Sect. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1016\/S0898-1221(02)00275-4","article-title":"Generalized hypergeometric functions associated with K-uniformly convex functions","volume":"44","author":"Gangadharan","year":"2002","journal-title":"Comput. Math. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"17","DOI":"10.5556\/j.tkjm.28.1997.4330","article-title":"On subclasses of uniformly convex functions and corresponding class of starlike functions","volume":"28","author":"Bharati","year":"1997","journal-title":"Tamkang J. Math."},{"key":"ref_26","first-page":"117","article-title":"On starlike functions associated with parabolic regions","volume":"45","year":"1991","journal-title":"Ann. Univ. Mariae Curie-Sk\u0142odowska Sect. Math."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/S0377-0427(99)00018-7","article-title":"Conic regions and k-uniform convexity","volume":"105","author":"Kanas","year":"1999","journal-title":"J. Comput. Appl. Math."},{"key":"ref_28","first-page":"647","article-title":"Conic regions and k-starlike functions","volume":"45","author":"Kanas","year":"2000","journal-title":"Rev. Roum. Math. Pure Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"87","DOI":"10.4064\/ap-56-1-87-92","article-title":"On uniformly convex functions","volume":"56","author":"Goodman","year":"1991","journal-title":"Ann. Polon. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/0022-247X(91)90006-L","article-title":"On uniformly starlike functions","volume":"155","author":"Goodman","year":"1991","journal-title":"J. Math. Anal. Appl."},{"key":"ref_31","first-page":"13","article-title":"Geometric properties of generalized Bessel functions of complex order","volume":"48","author":"Baricz","year":"2006","journal-title":"Mathematica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/s10013-014-0089-8","article-title":"Some Sufficient Conditions for Generalized Bessel Functions Associated with Conic Regions","volume":"43","author":"Porwal","year":"2015","journal-title":"Vietnam. J. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/662\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,29]],"date-time":"2024-05-29T04:25:09Z","timestamp":1716956709000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/6\/662"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,27]]},"references-count":32,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["sym16060662"],"URL":"https:\/\/doi.org\/10.3390\/sym16060662","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,5,27]]}}}